Documents

• Problem-solving tactics
• Mathematical induction   (.doc)  (pdf)
• Summation and product notation
• Lab 1
  On-Line Encyclopedia of Integer Sequences
  Maple
• Differential v. Difference Calculus
• Special Numbers
  • Iverson notation
  • Binomial coefficients
  • Stirling numbers of the first and second kinds
• Difference and divided difference tables
• Divided differences and the interpolating polynomial
• Lab 2: Spreadsheets & difference tables
• Operator calculus
• Sum of 4th powers via divided-difference table
• Integral v. summation calculus
• Fundamental Theorem of Discrete Calculus: the telescoping sum formula
• Summation-factor solution of first-order linear recurrence relations
• Lab 3:   Maple sum, int, and rsolve commands
• Asymptotics
• Asymptotics exercises
• and   answers
• Combinatorics
  • How to count
  • Counting problems
  • Counting problem answers
  • Four-fold Way
  • Twelve-fold Way
  • Sixteen-fold Way
• Probability
  • Probabilities and conditional probabilities of unions, intersections, and complements
  • Mean/expected value/expectation of a discrete random variable/distribution
  • Moments of a Discrete Random Variable/Distribution   ( htm) ( doc)
  • Special discrete probability distributions
  • Probability problems related to the basic discrete distributions
  • Discrete probability distributions and summation formulas
• Generating functions
  • Formulas 1, 2, 6, 7 of the top ten summation formulas are generating function formulas.
  • At the ice cream shoppe
  • Maple does generating functions.
    • In a terminal shell enter the following commands (noting the space dot at the end):
      cp ~holte/public/mcs256/demo.mw .
      xmaple &
    • From Maple, open demo.mw (now placed in your home directory).
    • Answer "Yes" to the autoexecute question.
    • Study the worked examples.
      Learn from them. Try to solve the extra problems in the demo.
• Recurrence relations
  • First-order linear recurrence relations
    • Solution by summation factor
    • Solution by unwinding/unfolding/backtracking
  • Linear recurrence relations with constant coefficients
  • Gambler's Ruin
  • Recurrences in Maple
• Top ten summation formulas